Related papers: Generalized Relativistic Kinematics
In a series of papers we proposed a model unifying general relativity and quantum mechanics. The idea was to deduce both general relativity and quantum mechanics from a noncommutative algebra ${\cal A}_{\Gamma}$ defined on a transformation…
The relativistic Lagrangian in presence of potentials was formulated directly from the metric, with the classical Lagrangian shown embedded within it. Using it we formulated covariant equations of motion, a deformed Euler-Lagrange equation,…
Recent work showed that $\kappa$-deformations can describe the quantum deformation of several relativistic models that have been proposed in the context of quantum gravity phenomenology. Starting from the Poincar\'e algebra of…
Starting from gravity as a Chern-Simons action for the AdS algebra in five dimensions, it is possible to deform the theory through an expansion of the Lie algebra that leads to a system consisting of the Einstein-Hilbert action plus…
A number of arguments at the interplay of general relativity and quantum theory suggest an operational limit to spatial resolution, conventionally modelled as a generalized uncertainty principle (GUP). Recently, it has been demonstrated…
Solutions of the sourceless Einstein's equation with weak and strong cosmological constants are discussed by using In\"on\"u-Wigner contractions of the de Sitter groups and spaces. The more usual case corresponds to a weak…
This paper summarizes and generalizes a recently proposed mathematical framework that unifies the standard formalisms of special relativity and quantum mechanics. The framework is based on Hilbert spaces H of functions of four space-time…
The second Poincar\'e kinematical group serves as one of new ones in addition to the known possible kinematics. The geometries with the second Poincar\'e symmetry is presented and their properties are analyzed. On the geometries, the new…
Relativistic deformed kinematics leads to a loss of the absolute locality of interactions. In previous studies, some models of noncommutative spacetimes in a two-particle system that implements locality were considered. In this work, we…
In the present paper we construct deformations of the Poincar\'e algebra as representations on a noncommutative spacetime with canonical commutation relations. These deformations are obtained by solving a set of conditions by an appropriate…
Metric theories of gravity are studied, beginning with a general action that is quadratic in curvature and allows infinite inverse powers of the d'Alembertian operator, resulting in infrared non-local extensions of general relativity. The…
In recent years, Planck-scale modifications to particles' dispersion relation have been deeply studied for the possibility to formulate some phenomenology of Planckian effects in astrophysical and cosmological frameworks. There are some…
The theory of the $\kappa$-deformed Poincare algebra is applied to the analysis of various phenomena in special relativity, quantum mechanics and field theory. The method relies on the development of series expansions in $\kappa^{-1}$ of…
The de Sitter invariant special relativity is a natural extension of the usual Einstein special relativity. Within this framework a generalization of special relativity (SR) for the de Sitter space-time introduces a new length scale $R$,…
Kinematic algebras can be realised on geometric spaces and constrain the physical models that can live on these spaces. Different types of kinematic algebras exist and we consider the interplay of these algebras for non-relativistic limits…
As a sequel to our previous work\cite{Feng2020}, we propose in this paper a quantization scheme for Dirac field in de Sitter spacetime. Our scheme is covariant under both general transformations and Lorentz transformations. We first present…
An extension of the finite and infinite Lie groups properties of complex numbers and functions of complex variable is proposed. This extension is performed exploiting hypercomplex number systems that follow the elementary algebra rules. In…
Quantization of relativistic point particles coupled to three-dimensional Einstein gravity naturally leads to field theories living on the Lorentz group in their momentum representation. The Lie group structure of momentum space can be…
The present article deals with a formulation of the so called (vacuum) Palatini gravity as a general variational principle. In order to accomplish this goal, some geometrical tools related to the geometry of the bundle of connections of the…
Weakening the Euclidean assumption in special relativity and the coordinate-independence hypothesis in general relativity for the de Sitter space, we propose a de Sitter invariant special relativity with two universal constants of speed $c$…